# Scalable Learning of Multivariate Distributions via Coresets

arXiv: https://arxiv.org/abs/2603.19792 · HTML: https://mlsanity.com/paper/2603.19792/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 51 references that are in the map.
- First posted on arXiv 20 Mar 2026.

## Builds on (most cited first, 28 of 28)

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Sketching as a Tool for Numerical Linear Algebra](https://mlsanity.com/paper/1411.4357/) (2014)
- [Turning Big data into tiny data: Constant-size coresets for k-means, PCA and projective clustering](https://mlsanity.com/paper/1807.04518/) (2018)
- [Coresets for Scalable Bayesian Logistic Regression](https://mlsanity.com/paper/1605.06423/) (2016)
- [Bayesian Coreset Construction via Greedy Iterative Geodesic Ascent](https://mlsanity.com/paper/1802.01737/) (2018)
- [On Coresets for Logistic Regression](https://mlsanity.com/paper/1805.08571/) (2018)
- [Coresets and Sketches](https://mlsanity.com/paper/1601.00617/) (2016)
- [Coresets for Near-Convex Functions](https://mlsanity.com/paper/2006.05482/) (2020)
- [Near-Optimal Coresets of Kernel Density Estimates](https://mlsanity.com/paper/1802.01751/) (2018)
- [Kernel Density Estimation through Density Constrained Near Neighbor Search](https://mlsanity.com/paper/2011.06997/) (2020)
- [Most Likely Transformations](https://mlsanity.com/paper/1508.06749/) (2015)
- [Oblivious sketching for logistic regression](https://mlsanity.com/paper/2107.06615/) (2021)
- [Amortized Projection Optimization for Sliced Wasserstein Generative Models](https://mlsanity.com/paper/2203.13417/) (2022)
- [p-Generalized Probit Regression and Scalable Maximum Likelihood Estimation via Sketching and Coresets](https://mlsanity.com/paper/2203.13568/) (2022)
- [Sparse Approximation via Generating Point Sets](https://mlsanity.com/paper/1507.02574/) (2015)
- [Improved Coresets for Kernel Density Estimates](https://mlsanity.com/paper/1710.04325/) (2017)
- [Multivariate Conditional Transformation Models](https://mlsanity.com/paper/1906.03151/) (2019)
- [Coresets for Regressions with Panel Data](https://mlsanity.com/paper/2011.00981/) (2020)
- [Almost Linear Constant-Factor Sketching for ℓ1 and Logistic Regression](https://mlsanity.com/paper/2304.00051/) (2023)
- [High-Dimensional Geometric Streaming in Polynomial Space](https://mlsanity.com/paper/2204.03790/) (2022)
- [Bayesian Conditional Transformation Models](https://mlsanity.com/paper/2012.11016/) (2020)
- [Optimal Sketching Bounds for Sparse Linear Regression](https://mlsanity.com/paper/2304.02261/) (2023)
- [Scalable Learning of Item Response Theory Models](https://mlsanity.com/paper/2403.00680/) (2024)
- [Random projections for Bayesian regression](https://mlsanity.com/paper/1504.06122/) (2015)
- [Optimal bounds for ℓp sensitivity sampling via ℓ2 augmentation](https://mlsanity.com/paper/2406.00328/) (2024)
- [Turnstile ℓp leverage score sampling with applications](https://mlsanity.com/paper/2406.00339/) (2024)
- [Graphical Transformation Models](https://mlsanity.com/paper/2503.17845/) (2025)
- [Data subsampling for Poisson regression with pth-root-link](https://mlsanity.com/paper/2410.22872/) (2024)

## Abstract (arXiv)

Efficient and scalable non-parametric or semi-parametric regression analysis and density estimation are of crucial importance to the fields of statistics and machine learning. However, available methods are limited in their ability to handle large-scale data. We address this issue by developing a novel coreset construction for multivariate conditional transformation models (MCTMs) to enhance their scalability and training efficiency. To the best of our knowledge, these are the first coresets for semi-parametric distributional models. Our approach yields substantial data reduction via importance sampling. It ensures with high probability that the log-likelihood remains within multiplicative error bounds of (1±varepsilon) and thereby maintains statistical model accuracy. Compared to conventional full-parametric models, where coresets have been incorporated before, our semi-parametric approach exhibits enhanced adaptability, particularly in scenarios where complex distributions and non-linear relationships are present, but not fully understood. To address numerical problems associated with normalizing logarithmic terms, we follow a geometric approximation based on the convex hull of input data. This ensures feasible, stable, and accurate inference in scenarios involving large amounts of data. Numerical experiments demonstrate substantially improved computational efficiency when handling large and complex datasets, thus laying the foundation for a broad range of applications within the statistics and machine learning communities.